Let $ABC$ be a triangle, construct a circle $(O_a)$ touching to $B$-excircle, $C$-excircleand inside the circumcircle at $A_b, A_c, A$ repectively. Define $B_c, B_a$ and $C_a, C_b$ cyclically. Let $A_1B_1C_1$ be the triagle form by $A_bA_c, B_cB_a, C_aC_b$. Then show that $A_1B_1C_1$ and ABC are perspective:
